The Two Axes of LLM Abstention: Answering Wrong vs. Answering Unanswerable Questions

An Overlooked Confusion

Ask ChatGPT: "Who won the 2024 Nobel Prize in Physics?" It confidently answers: "Einstein." — wrong.

Then ask: "Qin Shi Huang, who won the 2024 Nobel Prize in Physics?" It answers just as confidently: "Stephen Hawking." This time it's not that the answer is wrong — the question itself should not be answered.

Both failures look like "the model gave a wrong answer," but they are fundamentally different. The first is answering an answerable question incorrectly (a capability problem); the second is answering an unanswerable question (a judgment problem).

In July 2026, Benedikt J. Wagner from City St George's, University of London published an arXiv paper, Two Axes of LLM Abstention: Answer Correctness and Question Answerability, rigorously demonstrating that these two failure modes are orthogonal dimensions, and existing abstention mechanisms conflate them.

The Trap of a Single Confidence Score

Mainstream selective answering works like this: the model assigns each answer a confidence score and refuses to answer below a threshold. Sounds reasonable — if unsure, don't speak.

But Wagner found this conflates two fundamentally different things:

• Answer correctness: Am I confident in this answer?
• Question answerability: Can this question even be answered?

Using one threshold for both is like using one thermometer to measure both "is the food cooked" and "is the room cold" — both are "temperature," but the meanings are entirely different.

The paper ran a key experiment: across five instruction-tuned models (2B to 14B, from three model families), questions were divided into three classes:

• C (Correct-answerable): answerable, and answered correctly
• W (Wrong-answerable): answerable, but answered incorrectly
• U (Unanswerable): not answerable (e.g., "Qin Shi Huang's Nobel Prize")

If correctness and answerability were the same dimension, C, W, and U would lie on a single line. Instead, they form a crossed geometry — C and W separate on the correctness axis but nearly overlap on the answerability axis; U separates on the answerability axis, while its position on the correctness axis depends on implementation.

The two axes are independent.

Surface vs. Internal Signals: 0.54 vs. 0.97

The paper's most striking finding concerns where answerability signals live.

Researchers trained two kinds of answerability probes:

1. Output-layer probes: reading output confidence (e.g., softmax of logits) 2. Hidden-layer probes: reading intermediate-layer activations

The results differ dramatically:

• Output-layer probe AUROC: 0.54-0.67 (nearly random, with no improvement as model size grows)
• Hidden-layer probe AUROC: 0.97-0.99 (near-perfect)

This means: the model "knows" whether a question is answerable, but this knowledge is not reflected in its output confidence.

It's like a person who internally recognizes a trap question yet confidently answers anyway — their spoken words and internal judgment are disconnected.

More unsettling: output-layer AUROC shows no significant change from 2B to 14B. Scaling doesn't make models more "outwardly" honest — it makes their internal knowledge sharper, but that clarity doesn't propagate to the output.

CREPE: False Premises in the Wild

Beyond lab data, the paper tested a more realistic scenario: the CREPE dataset.

CREPE uses real user questions from Reddit's ELI5 (Explain Like I'm Five) board, some containing false premises. For example: "Why were there no spectators at the 2020 Tokyo Olympics?" — the premise is false; the games were postponed to 2021 but did have spectators.

These questions look perfectly normal and come from the same distribution as real questions, making surface-level detection hard.

Results on CREPE:

• Output-layer probes: 0.50-0.54 AUROC (essentially random)
• Elicited self-assessments (P(IK), P(True), direct premise checks): up to 0.67
• Internal linear probes: 0.69-0.77

The gap persists. Models can barely detect false premises "outwardly," but show some signal "internally" (hidden layers).

From Detection to Repair: 3x Precision Gain

Detection is only step one. Wagner then asked: can this finding fix abstention behavior?

The direct approach: have the model check premises first via a prompt — refuse if a false premise exists.

Result: the model challenged true and false premises at nearly the same rate — 57% of false premises were challenged, but many true premises were also misflagged. The model doesn't know *which* questions to challenge.

Wagner's clever fix: gate premise checking with the hidden-layer probe:

1. First use the hidden-layer probe to judge answerability 2. Only trigger the premise-check prompt if the probe flags the question as possibly unanswerable 3. If answerable, answer directly

Result: challenge precision improved 3x. The model stops challenging legitimate questions and precisely triggers checks only where problems may exist.

It's an elegant "internal-external combination": the hidden-layer probe does coarse screening; the premise-check prompt does fine review. Neither alone suffices, but combined they work significantly better.

Dual-Risk Certification: Formalizing Abstention

The final piece is formalization. Wagner reframes abstention as "three-class selective acceptance":

• Accept C (correctly answer answerable questions)
• Reject W (don't answer answerable questions you'd get wrong)
• Reject U (don't answer unanswerable questions)

Each class has its own budget:

• α_U = 0.15: at most 15% of unanswerable questions wrongly answered
• α_W = 0.50: at most 50% of answerable questions wrongly answered
• δ = 0.10: coverage of at least 10%

These budgets are certified with exact binomial confidence intervals, using a certification dataset separate from the probe training data — avoiding self-evaluation bias.

The certification reveals a scale-dependent asymmetry:

• The unanswerable budget was certifiable on 4 of 5 models
• The answerable budget is bounded by the model's own accuracy
• On an 8B model, a factored dual-threshold strategy certified both budgets simultaneously, with 0.75 coverage

This asymmetry shows: as models get stronger, the answerability dimension of abstention resolves naturally, but the correctness dimension remains capability-bound. Models can learn "don't answer the unanswerable," but "answer the answerable correctly" still requires capability gains.

An Analogy: The Hospital Triage Desk

Picture a hospital triage desk. The nurse makes two judgments:

1. Is this patient actually treatable? (answerability) — some "patients" aren't sick, or their symptoms are self-contradictory 2. If treatable, can we cure them? (correctness) — some diseases currently can't be cured

A triage desk using a single criterion (e.g., apparent severity) confuses these: lumping "untreatable serious illness" with "fake symptoms from a healthy person."

The better approach uses two independent checks — exactly Wagner's scheme: hidden-layer probes for triage, premise-check prompts for diagnosis.

Limitations and an Honest Assessment

The paper acknowledges several limitations:

1. Hidden-layer probe deployment cost: reading activations requires internal model access — infeasible for API-only, closed-source models like GPT-4. 2. Limited results on CREPE: even the best internal probe reaches only 0.77 AUROC — far from perfect. Real-world false-premise detection remains hard. 3. Blurry class boundaries: some questions sit between "answerable but hard" and "unanswerable." The paper uses hard labels; soft boundaries may be more realistic. 4. Conservative certification: exact binomial intervals are conservative; actual performance may be better. But conservative is the right choice in safety-critical settings.

The Bigger Picture: Two Dimensions of AI Honesty

The paper's significance goes beyond abstention techniques. It points to a deeper philosophical question: AI honesty has two dimensions.

The first layer: not saying wrong things — answer correctness.

The second layer: knowing when to stay silent — question answerability.

Current LLMs keep improving on the first layer, but progress on the second is slow — models tend to answer everything, even flawed questions.

Wagner's finding: these two layers are independent. A model can be accurate yet poor at judging whether a question should be answered, and vice versa. Moreover, models "know internally but don't say" — hidden layers carry the signal, outputs don't.

This echoes the Dunning-Kruger effect in humans — the incompetent don't know what they don't know. But Wagner's finding is subtler: the model knows it doesn't know; it just doesn't say so. This "knowing but not saying" gap is the next frontier of AI honesty research.

The paper's closing line is worth remembering: "Abstention is not one problem." In AI safety, many seemingly singular problems turn out to be multi-dimensional once decomposed. Acknowledging that multi-dimensionality is the first step toward building good safety mechanisms.

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Paper link: https://arxiv.org/abs/2607.08456

Author: Benedikt J. Wagner (City St George's, University of London)

Models tested: 5 instruction-tuned models, 2B-14B, from 3 model families

Published: July 9, 2026